It is often hard for me and for a lot of people to stop caring. You invest a lot of time into a job or relationship and when it starts going down the drain, it is hard to let go. You invest more time to salvage it, even if it seems impossible.
It is often good, and this approach saves what needs to be saved. On the other hand, you cannot save someone or something that does not want to be saved. If you see, that there is no try on the other side to even recognize a problem and try to fix it, then it is oke to stop caring.